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Hamaker Coefficient using Van der Waals Interaction Energy Formula

GoHamaker Coefficient using Potential Energy in Limit of Closest-Approach Formula

GoHamaker Coefficient using Van der Waals Forces between Objects Formula

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Hamaker coefficient A can be defined for a Van der Waals body–body interaction. Check FAQs

A = \frac{- U VWaals \cdot 6}{(\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 + R 2)}^{2})}) + (\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 - R 2)}^{2})}) + \ln (\frac{(z^{2}) - ({(R 1 + R 2)}^{2})}{(z^{2}) - ({(R 1 - R 2)}^{2})})}

A - Hamaker Coefficient?U_VWaals - Van der Waals interaction energy?R₁ - Radius of Spherical Body 1?R₂ - Radius of Spherical Body 2?z - Center-to-center Distance?

Hamaker Coefficient using Van der Waals Interaction Energy Example

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Here is how the Hamaker Coefficient using Van der Waals Interaction Energy equation looks like with Values.

Here is how the Hamaker Coefficient using Van der Waals Interaction Energy equation looks like with Units.

Here is how the Hamaker Coefficient using Van der Waals Interaction Energy equation looks like.

-88913.4178 = \frac{- 550 \cdot 6}{(\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 + 15)}^{2})}) + (\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 - 15)}^{2})}) + \ln (\frac{(40^{2}) - ({(12 + 15)}^{2})}{(40^{2}) - ({(12 - 15)}^{2})})}

-88913.4178J = \frac{- 550J \cdot 6}{(\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A + 15A)}^{2})}) + (\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A - 15A)}^{2})}) + \ln (\frac{({40A}^{2}) - ({(12A + 15A)}^{2})}{({40A}^{2}) - ({(12A - 15A)}^{2})})}

-88913.4178 = \frac{- 550 \cdot 6}{(\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 + 15)}^{2})}) + (\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 - 15)}^{2})}) + \ln (\frac{(40^{2}) - ({(12 + 15)}^{2})}{(40^{2}) - ({(12 - 15)}^{2})})}

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Hamaker Coefficient using Van der Waals Interaction Energy Solution

Follow our step by step solution on how to calculate Hamaker Coefficient using Van der Waals Interaction Energy?

FIRST Step Consider the formula

A = \frac{- U VWaals \cdot 6}{(\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 + R 2)}^{2})}) + (\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 - R 2)}^{2})}) + \ln (\frac{(z^{2}) - ({(R 1 + R 2)}^{2})}{(z^{2}) - ({(R 1 - R 2)}^{2})})}

Next Step Substitute values of Variables

∴

A = \frac{- 550J \cdot 6}{(\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A + 15A)}^{2})}) + (\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A - 15A)}^{2})}) + \ln (\frac{({40A}^{2}) - ({(12A + 15A)}^{2})}{({40A}^{2}) - ({(12A - 15A)}^{2})})}

Next Step Convert Units

∴

A = \frac{- 550J \cdot 6}{(\frac{2 \cdot 1.2E-9m \cdot 1.5E-9m}{({4E-9m}^{2}) - ({(1.2E-9m + 1.5E-9m)}^{2})}) + (\frac{2 \cdot 1.2E-9m \cdot 1.5E-9m}{({4E-9m}^{2}) - ({(1.2E-9m - 1.5E-9m)}^{2})}) + \ln (\frac{({4E-9m}^{2}) - ({(1.2E-9m + 1.5E-9m)}^{2})}{({4E-9m}^{2}) - ({(1.2E-9m - 1.5E-9m)}^{2})})}

Next Step Prepare to Evaluate

∴

A = \frac{- 550 \cdot 6}{(\frac{2 \cdot 1.2E-9 \cdot 1.5E-9}{({4E-9}^{2}) - ({(1.2E-9 + 1.5E-9)}^{2})}) + (\frac{2 \cdot 1.2E-9 \cdot 1.5E-9}{({4E-9}^{2}) - ({(1.2E-9 - 1.5E-9)}^{2})}) + \ln (\frac{({4E-9}^{2}) - ({(1.2E-9 + 1.5E-9)}^{2})}{({4E-9}^{2}) - ({(1.2E-9 - 1.5E-9)}^{2})})}

Next Step Evaluate

∴

A = -88913.4177708798J

LAST Step Rounding Answer

∴

A = -88913.4178J

Hamaker Coefficient using Van der Waals Interaction Energy Formula Elements

Variables

Functions

Hamaker Coefficient

Hamaker coefficient A can be defined for a Van der Waals body–body interaction.

Symbol: A

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Hamaker Coefficient

Van der Waals interaction energy

Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces.

Symbol: U_VWaals

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Van der Waals interaction energy

Radius of Spherical Body 1

Radius of Spherical Body 1 represented as R1.

Symbol: R₁

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Radius of Spherical Body 1

Radius of Spherical Body 2

Radius of Spherical Body 2 represented as R1.

Symbol: R₂

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Radius of Spherical Body 2

Center-to-center Distance

Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.

Symbol: z

Measurement: LengthUnit: A

Note: Value should be greater than 0.

Formulas to find Center-to-center Distance

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Hamaker Coefficient

Go Hamaker Coefficient using Potential Energy in Limit of Closest-Approach

A = \frac{- PE \cdot (R 1 + R 2) \cdot 6 \cdot r}{R 1 \cdot R 2}

Go Hamaker Coefficient using Van der Waals Forces between Objects

A = \frac{- F VWaals \cdot (R 1 + R 2) \cdot 6 \cdot (r^{2})}{R 1 \cdot R 2}

Other formulas in Hamaker Coefficient category

Go Hamaker Coefficient

A HC = (π^{2}) \cdot C \cdot ρ 1 \cdot ρ 2

How to Evaluate Hamaker Coefficient using Van der Waals Interaction Energy?

Hamaker Coefficient using Van der Waals Interaction Energy evaluator uses Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))) to evaluate the Hamaker Coefficient, The Hamaker coefficient using Van der Waals interaction energy A can be defined for a Van der Waals body–body interaction. Hamaker Coefficient is denoted by A symbol.

How to evaluate Hamaker Coefficient using Van der Waals Interaction Energy using this online evaluator? To use this online evaluator for Hamaker Coefficient using Van der Waals Interaction Energy, enter Van der Waals interaction energy (U_VWaals), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z) and hit the calculate button.

FAQs on Hamaker Coefficient using Van der Waals Interaction Energy

What is the formula to find Hamaker Coefficient using Van der Waals Interaction Energy?

The formula of Hamaker Coefficient using Van der Waals Interaction Energy is expressed as Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). Here is an example- -88913.417771 = (-550*6)/(((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09+1.5E-09)^2)))+((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09-1.5E-09)^2)))+ln(((4E-09^2)-((1.2E-09+1.5E-09)^2))/((4E-09^2)-((1.2E-09-1.5E-09)^2)))).

How to calculate Hamaker Coefficient using Van der Waals Interaction Energy?

With Van der Waals interaction energy (U_VWaals), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z) we can find Hamaker Coefficient using Van der Waals Interaction Energy using the formula - Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Hamaker Coefficient?

Here are the different ways to Calculate Hamaker Coefficient-

Hamaker Coefficient=(-Potential Energy*(Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Distance Between Surfaces)/(Radius of Spherical Body 1*Radius of Spherical Body 2)
Hamaker Coefficient=(-Van der Waals force*(Radius of Spherical Body 1+Radius of Spherical Body 2)*6*(Distance Between Surfaces^2))/(Radius of Spherical Body 1*Radius of Spherical Body 2)

Can the Hamaker Coefficient using Van der Waals Interaction Energy be negative?

Yes, the Hamaker Coefficient using Van der Waals Interaction Energy, measured in Energy can be negative.

Which unit is used to measure Hamaker Coefficient using Van der Waals Interaction Energy?

Hamaker Coefficient using Van der Waals Interaction Energy is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Hamaker Coefficient using Van der Waals Interaction Energy can be measured.

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Hamaker Coefficient using Van der Waals Interaction Energy Formula

​GoHamaker Coefficient using Potential Energy in Limit of Closest-Approach Formula

​GoHamaker Coefficient using Van der Waals Forces between Objects Formula

Hamaker Coefficient using Van der Waals Interaction Energy Example

Hamaker Coefficient using Van der Waals Interaction Energy Solution

Hamaker Coefficient using Van der Waals Interaction Energy Formula Elements

Other Formulas to find Hamaker Coefficient

Other formulas in Hamaker Coefficient category

How to Evaluate Hamaker Coefficient using Van der Waals Interaction Energy?

FAQs on Hamaker Coefficient using Van der Waals Interaction Energy

Variable Name

GoHamaker Coefficient using Potential Energy in Limit of Closest-Approach Formula

GoHamaker Coefficient using Van der Waals Forces between Objects Formula